Determination of liver function using the rate at which plasma disappears

ABSTRACT

A method and a device for determining liver function are described. 
     Liver function is determined after injection of an indicator dye into the bloodstream, optical measurement of the resulting concentration of indicator dye in the bloodstream and calculation of a plasma elimination rate from the dye concentration-time curve of the indicator dye. 
     An average circulation transit time mtt circ  is calculated from the measurement of the dye concentration c(t). In addition, a parameter k representing a fractional reentry rate of the indicator dye after each pass through the circulation is determined. The plasma elimination rate PER is calculated according to the equation: 
     
       
         PER=(1− k )/( k·mtt   circ ).

SUMMARY OF THE INVENTION

1. Field of the Invention

This invention concerns a method of determining liver function on thebasis of a plasma elimination rate and a device for determining liverfunction on the basis of a plasma elimination rate.

2. The Prior Art

Liver function is an important parameter in intensive care medicine andplays a crucial role in determining the prognosis for extremely illpatients. At the present time, liver function is determined routinely inintensive care medicine on the basis of various laboratory parameterswhich characterize the synthesis performance and the eliminationperformance of the liver. However, the disadvantage of these laboratoryvalues is that when liver function fails, these values do not becomepathological until after a rather long latency period, so the liverdysfunction does not become evident for several days.

One possibility of evaluating liver function immediately, at least withregard to elimination performance, consists of administering indicatorsubstances which are eliminated through the liver and determining theelimination time constant of these indicators. Indocyanine green is acommon indicator used for this purpose. Indocyanine green is usuallyinjected intravenously as a bolus, and then at least two blood samples,preferably several blood samples are taken at intervals of severalminutes over a period of at least 15 minutes following the bolusinjection. The elimination time constant can be calculated from the dropin indicator dye concentration in the blood specimens. However, thismethod is rarely used in clinical practice because it is still too timeconsuming because of the laboratory analyses.

SUMMARY OF THE INVENTION

The object of this invention is to create a method and a device withwhich liver function can be determined by non-invasively and themeasurement result is available more rapidly.

The method and the device according to this invention measure areduction in indicator concentration in the blood which occurs due todegradation of the indicator by the liver. After injecting a suitableindicator such as indocyanine green, into the bloodstream, acharacteristic indicator concentration-time curve is obtained at ameasurement point in the body when liver function is normal. First thereis an initial maximum indicator concentration, and after a temporarydecline, there is a second maximum indicator concentration. The secondmaximum occurs due to recirculation, i.e., a second pass is alreadyoccurring even before the concentration surge declines in the firstpass.

An average circulation transit time mtt_(circ) is calculated from themeasurement of the curve of the indicator concentration over time c(t),and in addition, a parameter k representing a fractional recovery rateof the indicator dye after each pass through the circulation is alsodetermined. Then with these values, the plasma elimination rate (PER)can be calculated according to the equation:

PER=(1−k)/(k·mtt _(circ))

The result is available after only a few recirculation cycles.

The average circulation transit time mtt_(circ) given above can becalculated from a circulation transport function g(t) which describesthe transport behavior of the circulation. The average circulationtransit time mtt_(circ) is then obtained according to the equation:${mtt}_{circ} = \frac{\int_{0}^{\infty}{{{g(t)} \cdot t}\quad {t}}}{\int_{0}^{\infty}{{g(t)}\quad {t}}}$

The circulation transport function g(t) can be calculated from themeasured indicator concentration with the help of an iterative nonlinearfitting method. In this method, with the stipulation of a modelfunction:

g(t)=a _(m) g _(m)(t)+a _(m+1) g _(m+1)(t)+ . . . +a _(n) g _(n)(t)

with ${{\sum\limits_{m = 1}^{n}\quad {am}} = 1},$

where the individual compartments amgm are described by left-skeweddistribution functions, a recursive convolution is performed accordingto the equations:

 c(t)=c _(bolus)(t)+c _(rez)(t)

and c_(rez)(t) = k ⋅ ∫₀^(t)g(t − u) ⋅ c(u)  u

where the parameters k, a_(m) and the parameters of the distributionfunctions are optimized by the method of the least squares deviation,with at least one compartment a₁g₁(t) being stipulated. In the equation,c(t) represents the concentration-time curve of the indicator dye,c_(bolus)(t) represents the first portion of the indicatorconcentration-time curve fitting directly to the measurement site,c_(rez)(t) denotes a recirculating portion of the indicatorconcentration-time curve and k denotes the elimination fraction of theindicator eliminated through the liver.

For a greater accuracy, two compartments (a₁g₁(t)) and (a₂g₂(t)) can bestipulated.

As an alternative, the optical measurement of the resulting indicatorconcentration in the bloodstream can be performed by fiber opticmeasurement in a central vessel or as a non-invasive method by measuringthe light transmission or reflection of incident light at suitable bodylocations, in particular on the finger, earlobe, bridge of the nose, theforehead or the inside of the cheek (buccal mucosa).

BRIEF DESCRIPTION OF THE DRAWINGS

This invention is explained in greater detail below with reference tothe drawing, which shows:

FIG. 1: a graphic plot of the concentration-time curve of an indicatordye,

FIG. 2: a semilogarithmic plot of the concentration-time curve accordingto FIG. 1,

FIG. 3: a graphic plot of the circulation transport function, and

FIG. 4: a block diagram of a device for measuring and determining theplasma elimination rate.

DETAILED DESCRIPTION OF THE PREFERRED EMBODIMENT

FIG. 1 shows a graphic plot of the concentration-time curve of anindicator dye after a bolus injection. The second maximum following thefirst maximum occurs due to recirculation, i.e., a second pass occursbefore the concentration surge subsides in a first pass.

Sensors connected to an analyzer circuit and a computer are arranged ata measurement point in the body to determine the indicator dyeconcentration-time curve. FIG. 4 shows an example of a device accordingto this invention. Two light transmitters 10 and 12 and two lightreceivers 14 and 16 are provided there and are connected to a computer20 via an analyzer circuit 18. It shall be assumed that indocyaninegreen is used as the indicator dye for the measurement of liverfunction.

Use of a reference dye is advantageous but is not absolutely necessary.Hemoglobin, the red pigment in blood, may be used as the reference dye.In this case, the one light transmitter 10 operates at a wavelength of800 nanometers (nm) and the other light transmitter 12 operates at awavelength of 900 nanometers. The light receivers 14 and 16 may bedesigned to filter out these wavelengths preferentially. As analternative, however, it is also possible to switch between two lighttransmitters 10 and 12, and in this case it is sufficient to have onlyone light receiver 14, but then it must be designed for bothwavelengths.

The absorption properties of the dyes can be measured by measuringeither the light transmission or the light reflection. Suitable sites onthe body include the fingers, the earlobes, the bridge of the nose, theforehead or the inside of the cheek.

The light intensity signals received by light receivers 14 and 16 areanalyzed by analyzer circuit 18 and sent to a computer 20. First thepulsatile components of the light intensities I_(ind puls)(t) andI_(ref puls)(t) are preprocessed in this computer 20, e.g., by formingthe quotient:

I _(ind puls)(t)=I _(ind)(t−dt)/I _(ind)(t+dt)

I _(ref puls)(t)=I _(ref)(t−dt)/I _(ref)(t+dt)

In another step, the relative dye concentration can be determined as afunction of time from these preprocessed signals, namely also by formingthe quotient:

c(t)=I _(ind puls) /I _(ref puls)

No calibration factor is needed here, because only one linear signal isneeded for the determination of the liver function. The measurementprinciple is not based on determination of absolute concentrationvalues, but instead is based only on determination of time constants.

Then in further analysis of the dye concentration as a function of time,a circulation transport function g(t) describing the transport behaviorof the circulation and a parameter k representing a functional reentryrate of the dye after each pass through the circulation are determinedfrom c(t) by means of nonlinear fitting algorithms.

The following discussion is based on a model where a transport path ofthe injected indicator dye ICG as a bolus injection leads first throughthe lungs. Downstream from the lungs, the transport path is divided intoa first rapid component, a second slow component and elimination of thedye through the liver. The first and second compartments then lead backto the lungs. The concentration of the indicator dye at the outlet ofthe lungs follows the function:

c(t)=c _(bolus)(t)+c _(rez)(t)

with c_(rez)(t) = k ⋅ ∫₀^(t)g(t − u) ⋅ c(u)  u

where c(t) represents the concentration-time curve of the indicator dye,c_(bolus)(t) represents the first portion of the dye concentration-timecurve fitting directly at the measurement site, c_(rez)(t) represents arecirculating portion of the dye concentration-time curve, and krepresents the fractional reentry rate of the dye after partialelimination through the liver. Therefore, the factor k is always smallerthan 1.

The transport process is described by a convolution integral.Recirculation in this model means that the result of the convolutionc_(rez)(t) also influences the input function c(t) at the same time.Recirculation of the indicator thus leads to a relationship which isdescribed in principle as follows:

 c(t)=f[k, g(t), c(t)]

The compartments of the circulation model are stipulated for g(t).Preliminary studies have shown that one to two compartments can bestipulated for dye dilution curves measured on patients for g(t),depending on the desired accuracy. This yields the following result forthe general model function:

g(t)=a _(m) g _(m)(t)+a _(m+1) g _(m+1)(t)+ . . . +a _(n) g _(n)(t)

with ${\sum\limits_{m = 1}^{n}\quad {am}} = 1$

where the individual compartments a_(m)g_(m) are described byleft-skewed distribution functions. The specific equation for twocompartments is:

g(t)=a ₁ g ₁(t)+a ₂ g ₂(t).

The circulation transport functions are calculated by computer frommeasured dye curves with the help of an iterative nonlinear fittingmethod, where with the stipulation of the model function:

g(t)=a ₁ g ₁(t)+a ₂ g ₂(t)

a recursive convolution is performed repeatedly according to theequations:

c(t)=c _(bolus)(t)+c _(rez)(t)

and c_(rez)(t) = k ⋅ ∫₀^(t)g(t − u) ⋅ c(u)  u

where k, a₁, a₂ and the parameters of the distribution functions areoptimized by the method of the least squares deviation.

After performing these computation steps, this yields a transportfunction such as that calculated as an example for the data for twocompartments as obtained in FIG. 1 and as plotted in FIG. 3. Theresulting transport function g(t) is composed of the transport functiong1(t) for the first compartment and g2(t) for the second compartment. Inaddition, the average circulation transit time (mtt_(circ)) which is thefirst moment of g(t), is calculated from the transport function g(t):${mtt}_{circ} = \frac{\int_{0}^{\infty}{{{g(t)} \cdot t}\quad {t}}}{\int_{0}^{\infty}{{g(t)}\quad {t}}}$

The plasma elimination rate (PER) of the indicator dye indocyanine greenis then obtained as follows:

PER=(1−k)/(k·mtt _(circ)).

An alternative method would be to determine the time constant K_(elim)of the elimination phase in the linear portion of the curve in thesemilogarithmic plot of the concentration-time curve according to FIG.2. In this case, the plasma elimination rate (PER) is:

 PER=K _(elim)/·100 ·60(for conversion to units /%/m).

What is claimed is:
 1. A method of determining liver function of apatient having a circulation on the basis of plasma elimination rate(PER), comprising the steps of: (a) injecting an indicator dye into abloodstream of said patient; (b) performing an optical measurement of aresulting concentration of indicator dye in the bloodstream; (c)calculating the plasma elimination rate (PER) from a dyeconcentration-time curve of the indicator dye; wherein calculating theplasma elimination rate (PER) includes: (i) calculating an averagecirculation transit time (mtt_(circ)) from the measurement of the dyeconcentration (c(t)); (ii) determining a parameter (k) representing afractional reentry rate of the indicator dye after each pass through thecirculation; and (iii) calculating the plasma elimination rate (PER)according to the equation PER=(1−k)/(k·mtt _(circ)).
 2. A methodaccording to claim 1, wherein calculating the average circulationtransit time (mtt_(circ)) is performed according to the equation${mtt}_{circ} = \frac{\int_{0}^{\infty}{{{g(t)} \cdot t}\quad {t}}}{\int_{0}^{\infty}{{g(t)}\quad {t}}}$

wherein g(t) is a circulation transport function which describes atransport behavior of the circulation.
 3. A method according to claim 2,wherein the circulation transport function g(t) is calculated from themeasured dye concentration employing an iterative nonlinear fittingmethod which includes performing repeatedly a recursive convolutionaccording to the equations c(t)=c _(bolus)(t)+c _(rez)(t) andc_(rez)(t) = k ⋅ ∫₀^(t)g(t − u) ⋅ c(u)  u

wherein c(t) represents the concentration-time curve of the indicatordye, c_(bolus)(t) represents a first fraction of the dyeconcentration-time curve directly at the measurement site, c_(rez)(t)represents a recirculating fraction of the dye concentration-time curve,k represents a fractional reentry rate of the dye due to eliminationthrough the liver, and wherein a model function g(t)=a _(m) g _(m)(t)+a_(m+1) g _(m+1)(t)+ . . . +a _(n) g _(n)(t) with${\sum\limits_{m = 1}^{n}\quad {am}} = 1$

is stipulated with individual compartments, a_(m)g_(m) being describedby left-skewed distribution functions and at least one compartmenta₁g₁(t) being stipulated, wherein k and a_(m) and parameters ofdistribution functions are optimized according to a least squaredeviation method.
 4. A method according to claim 3, wherein twocompartments a₁g₁(t)+a₂g₂(t) are stipulated.
 5. A method according toclaim 1, wherein the optical measurement of the resulting dyeconcentration in the bloodstream is performed by means of a fiber opticmeasurement in a central vessel.
 6. A method according to claim 1,wherein the optical measurement of the resulting dye concentration inthe bloodstream is performed by measuring one of the group of: lighttransmission and reflection of incident light in a non-invasive way at asuitable location on the body comprising a finger, earlobe, bridge ofnose, buccal mucosa or forehead.
 7. A device for determining liverfunction of a patient having a circulation on the basis of plasmaelimination rate (PER), comprising: (a) an optical measurement sensorfor determining an indicator dye concentration in a bloodstream of thepatient resulting from an injection of indicator dye into thebloodstream; and (b) a computer for determining the plasma eliminationrate (PER) from a dye concentration-time curve of the indicator dye,wherein the computer is controlled such that an average circulationtransit time (mtt_(circ)) is calculated from the measurement of the dyeconcentration (c(t)); a parameter (k) representing a fractional reentryrate of the indicator dye after each pass through the circulation isdetermined, and the plasma elimination rate (PER) is calculatedaccording to the equation PER=(1−k)/(k·mtt _(circ)).
 8. A deviceaccording to claim 7, wherein the computer is controlled such thatcalculating the average circulation transit time (mtt_(circ)) isperformed according to the equation${mtt}_{circ} = \frac{\int_{0}^{\infty}{{{g(t)} \cdot t}\quad {t}}}{\int_{0}^{\infty}{{g(t)}\quad {t}}}$

wherein g(t) is a circulation transport function which describestransport behavior of the circulation.
 9. A device according to claim 8,wherein the computer is controlled such that the circulation transportfunction g(t) is calculated from the measured dye concentrationemploying an iterative nonlinear fitting method which includesperforming repeatedly a recursive convolution according to the equationsc(t)=c _(bolus)(t)+c _(rez)(t) andc_(rez)(t) = k ⋅ ∫₀^(t)g(t − u) ⋅ c(u)  u

wherein c(t) represents the concentration-time curve of the indicatordye, c_(bolus)(t) represents a first fraction of the dyeconcentration-time curve directly at the measurement site c_(rez)(t)represents a recirculating fraction of the dye concentration-time curvek represents a fractional reentry rate of the dye due to eliminationthrough the liver and wherein a model function g(t)=a _(m) g _(m)(t)+a_(m+1) g _(m+1)(t)+ . . . +a _(n) g _(n)(t) with${\sum\limits_{m = 1}^{n}\quad {am}} = 1$

is stipulated with individual compartments, a_(m)g_(m) being describedby left-skewed distribution functions and at least one compartmenta₁g₁(t) being stipulated, wherein k and a_(m) and parameters ofdistribution functions are optimized according to a least squaredeviation method.
 10. A device according to claim 9, wherein thecomputer is controlled such that two compartments a₁g₁(t)+a₂g₂(t) arestipulated.
 11. A device according to claim 7, wherein the opticalmeasurement sensor is a fiberoptic catheter adapted for being arrangedin a central vessel for performing the measurement.
 12. A deviceaccording to claim 7, wherein the optical measurement sensor includes: alight transmitter and a light receiver, both of said light transmitterand light receiver being adapted to measure one of the group of: lighttransmission and reflection of incident light in a non-invasive way at asuitable location on the body comprising a finger, earlobe, bridge ofnose, inside of cheek or forehead.